Generally, I can read and understand sentences with conditionals (ba, to, tara, nara). However, I don't understand the different nuances between them. Can someone please give me a general overview of these differences?

All of the following is just according to my understanding which is by no means perfect:

You use ～ば when setting up a hypothetical situation in which your conditional would be fulfilled, which may not be certain.e.g.思い出せば、教えます。In the hypothetical situation that I remember, I'll tell you.or, more elegantly in English:Should/If I remember, I'll tell you.

You use ～たら when setting up a conditional to do with constrained conditions (not sure how to explain this better, sorry!)よかったら、友達になりましょう！If it's OK with you, let's become friends!In this case, 'become friends' is constrained by 'OK with you'

You use ～と when it's not REALLY a conditional (we just use if/when in English for some reason), but when it's a logical consequence, not dependent on anything really.試験落ちると大学に行けませんIf you fail exams, you can't go to university.Here we're not actually talking about any hypothetical situation, 'failing exams' and 'unable to go to university' are inseparable cause and effect.

I think なら〔ならば〕 falls into the ～ば form, though I am not too sure. It's basically the ～ば form of だ（じゃない、だったら、など）, which means you can use it with not just verbs but everything.サッカーなら、あまり遊びたくありません。In the case of football, I don't really want to play.胸が痛む〔の〕なら、病院に行きな！If your chest hurts, go to the hospital!青い〔の〕なら、欲しいです！If it's blue, I want it!

I think in the last two cases, it is the same thing to use ～ば (e.g., 胸が痛めば、青ければ), though I am not too sure on this.

I have the Basic and Intermediate Grammar Dictionaries by Seiichi Makino and Michio Tsutsui, and I like them very much. I definitely recommend them. I read the whole Basic book twice, and I'm working my way through the Intermediate one. Conditionals were about the only thing I found some difficulty in. I did understand them individually but I wasn't clear about the differences.

I think that the one that was more challenging was たら. It seems to me that the emphasis is on the consequence? With the example given,

よかったら、友達になりましょう！Let's become friends............... if it's OK with you

Of course, it sounds more natural in English if translated as takirasさん did:If it's OK with you, let's become friends!